A relay race is 1 /4 space m i l e s.

There are three relay runners on the team.

Each person runs the same distance.

How far does each person run?

a. He did not distribute the negative sign, which resulted in changing the signs of the terms inside the parentheses.

b. The correct simplification of the expression is 33-20x.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

a. Victor made an error in the second step where he distributed only the coefficient 4 to both terms inside the parentheses. However, he did not distribute the negative sign, which resulted in changing the signs of the terms inside the parentheses.

b. To correct Victor's work, we need to distribute both the coefficient 4 and the negative sign to all the terms inside the parentheses, which gives us:

9 - 4(5x - 6)

9 - 20x + 24 (distribute)

33 - 20x (combine like terms)

Therefore, the correct simplification of the expression is 33-20x.

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Answer: 1second

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.

the total cost of leather purchased to make the football is $30.79.

The volume of a football can be calculated using the formula for the volume of a sphere:

V = (4/3)πr³

Where r is the radius

Given that the diameter of the football is 14 cm and  the radius is half of the diameter, so radius is 7 cm.

So, the volume of the football is:

V = (4/3)π(7 cm)³

= 1437.33 cm³

Now, we know that 3% of the leather is wasted,

so the amount of leather to make the football is:

(100% - 3%) = 97% of the total leather purchased.

Therefore, the amount of leather used to make the football is:

0.97 × 1437.33 cm³ = 1394.19 cm³

To find the total cost of the leather purchased, we need to know the cost of leather per square centimeter. Let's assume that the cost of leather including labor is $0.05 per square centimeter.

The surface area of a sphere can be calculated using the formula:

A = 4πr²

So, the surface area of the football is:

A = 4π(7 cm)²

= 615.75 cm²

the total cost of the leather:

Cost of leather = Cost per square centimeter × Surface area of the football

= $0.05/cm² × 615.75 cm²

= $30.79

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The linear equatiοn has infinite sοlutiοns.

When twο expressiοns are jοined by the equal sign ('='), a mathematical statement is created. In οrder tο be determined, there must be at least οne unknοwn variable. An equatiοn is sοmething like 3x - 8 = 16. This equatiοn can be sοlved tο yield x = 8.Any οne variable linear equatiοns can have zerο, οne οr infinite sοlutiοns.

Emma substitutes 3 fοr x in a οne-variable linear equatiοn and finds that it makes the equatiοn true. She then substitutes 5 fοr x in the same linear equatiοn and finds that 5 alsο makes the equatiοn true.

If Emma tested twο values 3 and 5 fοr the same οne variable linear equatiοn and they were bοth true sοlutiοns, this means that the equatiοn has mοre than οne sοlutiοn.

If a οne variable linear equatiοn has mοre than οne sοlutiοn, than the equatiοn has infinite sοlutiοns.

Hence, the linear equatiοn Emma is talking abοut has infinite number οf sοlutiοns.

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The flux density is 3000 uT.

Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.

It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.

The flux density (B) can be calculated using the fοrmula:

B = Φ / A

where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.

Plugging in the values given, we get:

B = 1500 uWb / 0.5 m²

B = 3000 uT (micrοtesla)

Therefοre, the flux density is 3000 uT.

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The average rate of change of the function is 3.

The average rate of change of a function is given by the formula:

average of change = (f(b) - f(a)) / (b - a)

Where [a, b] is the interval of the function

f(x) = x³ + 2x;  [-1, 1]

average rate of  change = ([ 1³ + 2(1)] - [ (-1)³ + 2(-1)]) / (1 - (-1))

average rate of change = (3 - (-3))/(1 + 1)

average rate of change = 6/2

average rate of change = 3

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Answer: We can simplify the expression by using the identity for the tangent of half an angle:

tan(x/2) = sin(x) / (1 + cos(x))

where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.

So, we have:

sin(28°) / (1 + cos(28°)) = tan(56°/2)

We know that 56°/2 = 28°, so we have:

tan(28°)

Therefore, the expression simplifies to a single trigonometric function:

tan(28°)

Step-by-step explanation:

Answer: 175

Step-by-step explanation:

[tex] \:\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{Circumference\: of\: circle = 2πr}\\[/tex]

As per question, the radius of a circle is 13 in and we are asked to find out it's circumference in terms of π. Here-

Now that we are given the value of radius of the circle, so we can substitute it into the formula and solve for circumference-

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 2\pi r}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Circumference_{( circle)} = 2 \times \pi \times 13\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 26 \pi \:inch}\\[/tex]

Answer: 3.625 or 3 5/8

Step-by-step explanation:

So I personally would turn everything into decimals and subtract.

21.250 -17.625

And using our handy calculator, you get

3.625

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

What is meant by budget?

In general, a budget is a financial plan or estimate that outlines the expected income and expenses over a specific period.

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

In scenario 1, Carlos chose a more expensive cereal because he recognized it from a TV commercial, which may have influenced his perception of its quality or desirability.

In scenario 2, Evelyn decided not to purchase a plane ticket because the prices were too high for her budget, despite there being multiple airlines offering flights to London.

Therefore,The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

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Answer:

  [tex]\frac{20}{19}[/tex] or ≈ 1.053

Step-by-step explanation:

We Know

220 responded 'yes', and 209 responded 'no'

Find the probability that if a person is chosen at random, they had run a red light in the last year.

The probability is: [tex]\frac{220}{209}[/tex] = [tex]\frac{20}{19}[/tex] ≈ 1.053

So, the answer is [tex]\frac{20}{19}[/tex] or ≈ 1.053

Answer:A

Step-by-step explanation: i have had this question before

Answer:

A

Step-by-step explanation:

A proportion is given:

[tex] \frac{4}{5} = \frac{ {x}^{2} }{20} [/tex]

Use the property of proportion to find x (cross-multiply):

[tex]5 \times {x}^{2} = 20 \times 4[/tex]

[tex]5 {x}^{2} = 80[/tex]

Divide both sides of the equation by 5 to make x^2 the subject:

[tex] {x}^{2} = 16[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{16} = 4[/tex]

The Null hypothesis is that the population mean depression score of all college students is less than or equal to 38 (H₀: µ ≤ 38) while the Alternative hypothesis is that the population mean depression score of all college students is greater than 38 (Ha: µ > 38).

Null hypothesis: The population mean depression score of all college students is less than or equal to 38 (H₀: µ ≤ 38).

Alternative hypothesis: The population mean depression score of all college students is greater than 38 (Ha: µ > 38).

Step 2: Test statistic

We will use a one-sample t-test since the population standard deviation is known and the sample size is greater than 30. The test statistic is calculated as:

t = (x - µ) / (σ / √(n))

where x is the sample mean, µ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the numbers, we get:

t = (40 - 38) / (16 / √(64))

t = 2

Step 3: P-value

Using a t-table with 63 degrees of freedom (df = n - 1), we find the p-value for a one-tailed test with a t-value of 2 is approximately 0.025.

Step 4: Decision

Since the p-value (0.025) is less than the alpha level (0.025), we reject the null hypothesis.

Step 5: Conclusion

There is sufficient evidence to suggest that the population mean depression score of all college students is greater than 38.

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Rolle’s Theorem can be applied to the closed interval.

What is the Rolle’s Theorem?

In essence, Rolle's theorem or Rolle's lemma argues that there must be at least one stationary point—a position where the first derivative is zero—between any two separate sites where a real-valued differentiable function achieves equal values. The theorem bears Michel Rolle's name.

Here, we have

Given: f(x) = -x² + 3x, [0,3]

We must determine whether Rolle’s Theorem can be applied to the closed interval.

f(x) is continuous in the closed interval  [0,3].

f(x) is differentiable in the open interval (0,3)

f(0) = 0 + 0 = 0

Rolle's theorem can be applied.

f'(x) = -2x + 3

f'(x) = 0

-2x + 3 = 0

3 = 2x

x = 2/3

2/3 lies inside the [0,3].

Hence, Rolle’s Theorem can be applied to the closed interval.

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Option D is equivalent to 30 - 29m, which is equivalent to option B (8 / m) only if m is not equal to zero.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

In the given options, option A and B are not equivalent, option C is not equivalent to any other option, and option D is equivalent to option B.

Option A can be written as 5m + 35 using the distributive property of multiplication over addition.

Option B can be simplified as follows:

(15 - 7) / m = 8 / m

Therefore, option B is equivalent to 8 / m.

Option C cannot be simplified to any other expression in the given options.

Option D can be simplified as follows:

30 - (m * 29) = 30 - 29m

Therefore, option D is equivalent to 30 - 29m, which is equivalent to option B (8 / m) only if m is not equal to zero.

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Answer:

C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

Using properties of square,

a. Equation for total area = 2x² - 16x + 64

b. Area will be minimum for the value of x = 0

c. Minimum area will be 64cm².

With four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.

Total length of wire = 32cm.

Now side of one square is given as x.

Perimeter of big square will be = 4x.

Now perimeter of small square = 32- 4x.

Side of small square = (32-4x)/4

= 4(8-x)/4

= 8-x

Area of big square = x × x

= x².

Area of small square = (8-x) ².

Now Total area, A(x) = x² + (8-x) ²

= x² + 64 + x² - 16x

= 2x² - 16x + 64

The side length that will minimize the area will be, x = 0.

Minimum area of the total figure will be = 64cm²

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The measure of angle m<BAC = 110 and the measure of angle m<ABC = 35.

The angle sum property of the triangle state that the sum of interior angles of triangles is 180.

<CDB = 55 (Given)

By degree measure theorem

<CAB = 2 <CDB

<CAB = 2 * 55 = 110

Again AC = AB (Radius of the circle)

Then

<ACB = <ABC (angles opposite to equal sides)

let <ACB = m

In triangle ACB,

By angle sum property: <ACB + <ABC + <CAB =180

m + m + 100 = 180

2m = 180 - 110

2m = 70

m = 70/2 = 35

<ACB = <ABC = 35

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Ruth will have the principal is approximately $5,534.04 in 1 year at earns 12% interest compounded annually.

What is principal?

To find how much Ruth will have in 1 year, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{n*t}[/tex]

where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:

A =  [tex]$4,942(1 + 0.12/1)^{1*1}[/tex]

A = $4,942(1.12)

A = $5,534.04

Therefore, Ruth will have approximately $5,534.04 in 1 year.

What is an interest?

Interest is the amount of money charged by a lender to a borrower for the use of money over a period of time. It is typically calculated as a percentage of the amount borrowed or invested, and is often expressed as an annual percentage rate (APR). Interest can be simple or compound, depending on whether it is calculated only on the principal amount or on both the principal and accumulated interest. Interest is an important concept in finance and economics, and is used in a wide range of financial transactions, including loans, investments, and savings accounts.

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Answer:

15 cm (shorter side)

50 cm (longer side)

Step-by-step explanation:

Let the length of the shorter side of the parallelogram be x cm. Then, the length of the longer side is (2x + 20) cm. Since a parallelogram has opposite sides equal in length, there will be two shorter sides and two longer sides.

The perimeter of the parallelogram is given as 130 cm. The sum of the lengths of all four sides is equal to the perimeter. Therefore, we can set up the following equation:

2x + 2(2x + 20) = 130

Now, we can solve for x:

2x + 4x + 40 = 130

6x + 40 = 130

6x = 130 - 40

6x = 90

x = 90/6

x = 15

Now that we have found the length of the shorter side (x), we can find the length of the longer side:

Longer side = 2x + 20 = 2(15) + 20 = 30 + 20 = 50

So, the dimensions of the parallelogram are 15 cm (shorter side) and 50 cm (longer side).

The dimensions of the parallelogram are 15 cm x 50 cm.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.

Given that, in a parallelogram, the longer side is 20 cm longer than twice the shorter side. the perimeter is 130 cm.

We need to find the dimension of the parallelogram,

Let the length of the shorter side of the parallelogram be x cm.

Then, the length of the longer side is (2x + 20) cm.

The perimeter of the parallelogram is given as 130 cm.

Therefore, we can set up the following equation:

2x + 2(2x + 20) = 130

Now, we can solve for x:

2x + 4x + 40 = 130

6x + 40 = 130

6x = 130 - 40

6x = 90

x = 90/6

x = 15

Longer side = 2x + 20 = 2(15) + 20 = 30 + 20 = 50

Hence, the dimensions of the parallelogram are 15 cm x 50 cm.

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Answer:

linear function

Step-by-step explanation:

straight line then add up

Answer:

Step-by-step explanation:

In (b) you may be more used to the formula for arc length: [tex]P=\frac{\theta }{180} \times \pi r[/tex].

The result is the same.

In this case, Bridget's commission rate is 5%, which can also be written as   [tex]0.05[/tex] (since 5% is equivalent to 5/100 or 0.05 as a decimal).  Bridget earned a commission of $ [tex]16[/tex] on the sale of the television.

To calculate the commission that Bridget earned, we can use the formula:

commission [tex]= (percentage/100) \times sale price[/tex]

where the sale price is the price of the television that Bridget sold, and the percentage is the commission rate, which is 5%.

Using this formula, we can calculate the commission as:

commission[tex]= (5/100) \times $320 = $16[/tex]

Therefore, Bridget earned a commission of $  [tex]16[/tex] on the sale of the television.

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[tex]Step-by-step-explanation-& Answer[/tex]

Well if our friend Rick continues the pattern that is shown in the question then the answer is at the bottom

Lets do some addition:

(6+3) * 5 ( 5 x 2 = 10 )

First find the parenthesis, 6 + 3 = 9

Next multiply, 9 x 5 = 45

Thus the answer to your problem is:

[tex]\left[\begin{array}{ccc}A&N&S\\=&=&=\\4&5&!\end{array}\right][/tex]

Answer: To obtain triangle A'B'C' from triangle ABC by reflection over the line y = 2, we reflect each point of the triangle over the line. This gives us:

A' = (A_x, 4 - A_y)

B' = (B_x, 4 - B_y)

C' = (C_x, 4 - C_y)

To obtain triangle A"B"C" from triangle A'B'C' by translation by the directed line segment from (0,0) to (3,2), we add the vector (3,2) to each point of the triangle. This gives us:

A" = (A'_x + 3, A'_y + 2) = (A_x + 3, 6 - A_y)

B" = (B'_x + 3, B'_y + 2) = (B_x + 3, 6 - B_y)

C" = (C'_x + 3, C'_y + 2) = (C_x + 3, 6 - C_y)

Therefore, the vertices of triangle A"B"C" are (A_x + 3, 6 - A_y), (B_x + 3, 6 - B_y), and (C_x + 3, 6 - C_y).

Step-by-step explanation:

Answer:

2 triangles, 180 for each triangle and 360 degrees in a square

Option C) 0 <= x <= 12 and 16 <= y <= 48 would be reasonable constraints for the context.

What is the inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The x-axis represents the number of hours since 9 AM, which can range from 0 to 12 since the shift ends at 9 PM.

The y-axis represents the number of patients, which can realistically range from 16 to 48 as hospitals can have varying levels of patient traffic.

The constraint includes the endpoints of the range, which makes it more accurate.

Hence, Option C) 0 <= x <= 12 and 16 <= y <= 48 would be reasonable constraints for the context.

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Answer:

A.998

Step-by-step explanation:

256 times 4 =1024-26=998 the facts that she uses 16 beads on each necklace is useless